Related papers: On the Need for Large Quantum Depth
It has previously been established that the logarithmic-depth approximate quantum Fourier transform (AQFT) provides a suitable replacement for the regular QFT in many quantum algorithms. Since the AQFT is less accurate by definition,…
The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in…
Digital quantum computers promise exponential speedups in performing quantum time-evolution, providing an opportunity to simulate quantum dynamics of complex systems in physics and chemistry. However, the task of extracting desired quantum…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum…
As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…
Quantum computing promises potential for science and industry by solving certain computationally complex problems faster than classical computers. Quantum computing systems evolved from monolithic systems towards modular architectures…
Consider the model of computation where we start with two halves of a $2n$-qubit maximally entangled state. We get to apply a universal quantum computation on one half, measure both halves at the end, and perform classical postprocessing.…
Parallelization is a major challenge in quantum algorithms due to physical constraints like no-cloning. This is vividly illustrated by the conjecture of Moore and Nilsson from their seminal work on quantum circuit complexity [MN01,…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…
Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve practical quantum advantages. However, the presence of quantum noise might suppress and undermine these advantages, which blurs the…
In the NISQ-era of quantum computing, we should not expect to see quantum devices that provide an exponential improvement in runtime for practical problems, due to the lack of error correction and small number of qubits available.…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
Quantum algorithms for simulating large and complex molecular systems are still in their infancy, and surpassing state-of-the-art classical techniques remains an ever-receding goal post. A promising avenue of inquiry in the meanwhile is to…
The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are…
We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row…
This paper shows that, in measurement-based quantum computation, it is possible to write any quantum oracle implementing a classical function in constant depth. The result is shown through the equivalence between MBQC and the circuit model…
In recent years, the number of hybrid algorithms that combine quantum and classical computations has been continuously increasing. These two approaches to computing can mutually enhance each others' performances thus bringing the promise of…